Probability Distributions
A probability distribution tells you how likely each possible outcome is. Think of it as a recipe that assigns a probability to every value a random variable can take. Two of the most common distributions in AI are the Normal (Gaussian) and Binomial distributions.
A probability distribution describes the likelihood of each possible outcome of a random process.
Discrete vs. Continuous Distributions
- Discrete: Outcomes are countable (e.g., number of heads in 3 coin flips: 0,1,2,3).
- Continuous: Outcomes can be any value in a range (e.g., height, temperature).
Normal Distribution (Bell Curve)
The normal distribution is the most famous continuous distribution. It is symmetric and bell‑shaped. Many real‑world phenomena follow it: heights, test scores, measurement errors.
- Mean (μ): Center of the curve.
- Standard deviation (σ): Spread of the curve.
- 68% of data falls within 1σ of the mean, 95% within 2σ, 99.7% within 3σ (Empirical Rule).
Binomial Distribution
The binomial distribution models the number of successes in a fixed number of independent trials, each with the same probability of success. Example: flipping a coin 10 times, counting heads.
- n = number of trials
- p = probability of success per trial
Why Distributions Matter in AI
- Data understanding: Knowing the distribution helps choose appropriate algorithms.
- Generative models: Models like GANs learn to generate data from a distribution.
- Anomaly detection: Unusual data points are those with very low probability under the distribution.
Two Minute Drill
- A probability distribution assigns probabilities to all possible outcomes.
- Normal distribution: bell curve, symmetric, defined by mean and standard deviation.
- Binomial distribution: counts successes in fixed trials.
- Distributions are used to model data, initialize weights, and detect anomalies.
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